Research Expertise

Description

My research deals with fundamental aspects of gauge theory, gravity and string theory. I am in particular interested in the quantum spectra of non-perturbative objects of these theories, such as instantons, monopoles, black holes and D-branes. Two directions of my past and current research are: 1) Bound states of fundamental constituents: supersymmetric gauge and gravity theories have a rich spectrum of so-called Bogomolny'i-Prasad-Sommerfield bound states of their fundamental constituents. The degrees of freedom associated with the bound state can be described using the mathematics of quiver representation theory. 2) Partition functions of Yang-Mills theory and supergravity: Partition functions contain crucial information about quantum spectra and are indispensable tools to address questions about entropy, phase transitions, symmetries and dualities of the physical theories. These symmetries and dualities imply interesting number theoretic properties for the partition functions. Supersymmetric quantum spectra typically depend discontinuously on external parameters J (a phenomena also known as wall-crossing). This is captured by partition functions through sums over an indefinite lattice.